%I #21 Sep 08 2022 08:44:43
%S 1,0,0,1,1,1,2,3,4,6,8,12,18,25,36,53,76,109,158,228,329,475,685,989,
%T 1428,2060,2973,4292,6194,8939,12902,18621,26875,38788,55981,80796,
%U 116611,168300,242902,350574,505972
%N Expansion of 1/(1-x^3-x^4-x^5-x^6-x^7-x^8-x^9).
%C Number of compositions (ordered partitions) of n into parts 3, 4, 5, 6, 7, 8 and 9. - _Ilya Gutkovskiy_, May 25 2017
%H Vincenzo Librandi, <a href="/A017822/b017822.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,1,1,1,1,1,1).
%F a(n) = a(n-3) +a(n-4) +a(n-5) +a(n-6) +a(n-7) +a(n-8) +a(n-9) for n>8. - _Vincenzo Librandi_, Jun 27 2013
%t CoefficientList[Series[1 / (1 - Total[x^Range[3, 9]]), {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 27 2013 *)
%t LinearRecurrence[{0,0,1,1,1,1,1,1,1},{1,0,0,1,1,1,2,3,4},50] (* _Harvey P. Dale_, Feb 04 2015 *)
%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x^3-x^4-x^5-x^6-x^7-x^8-x^9)))); /* or */ I:=[1,0,0,1,1,1,2,3,4]; [n le 9 select I[n] else Self(n-3)+Self(n-4)+Self(n-5)+Self(n-6)+Self(n-7)+Self(n-8)+Self(n-9): n in [1..50]]; // _Vincenzo Librandi_, Jun 27 2013
%K nonn,easy
%O 0,7
%A _N. J. A. Sloane_.